Abstract
Taking the flat-space limit (zero cosmological constant limit) of the Rindler-AdS spacetime yields the Rindler metric. According to the proposal of Flat/contracted-CFT correspondence, the flat-space limit on the bulk side of asymptotically AdS spacetimes corresponds to the contraction of the conformal field theory on the boundary. We use this proposal for the Rindler-AdS/CFT correspondence and propose a dual theory for the Rindler spacetime, which is a contracted conformal field theory (CCFT). We show that the two-dimensional CCFT symmetries exactly predict the same two-point functions that one may find by taking the flat-space limit of three-dimensional Rindler-AdS holographic results. Using the Flat/CCFT proposal, we also calculate the three-dimensional Rindler energy-momentum tensor. Since the near horizon geometry of non-extreme black holes has a Rindler part, we note that it is plausible to find a dual CCFT at the horizon of non-extreme black holes. By using our energy-momentum tensor, we find the correct mass of non-rotating BTZ and show that the Cardy-like formula for CCFT yields the Bekenstein-Hawking entropy of non-extreme BTZ. Our current work is the first step towards describing the entropy of non-extreme black holes in terms of CCFTs microstates which live on the horizon.
Highlights
As another check for the Flat/contracted conformal field theory (CCFT) correspondence, one can take the flat limit of the Rindler-AdS/CFT correspondence
We show that the two-dimensional CCFT symmetries exactly predict the same two-point functions that one may find by taking the flat-space limit of three-dimensional Rindler-AdS holographic results
We repeat the same procedure for the three-dimensional Rindler spacetimes and find non-zero components of the stress tensor which can be used in the calculation of conserved charges by using Brown and York’s method [20]
Summary
The time coordinate of the metric (2.1) is the proper time of an observer which is located at r = r0 = The temperature which these observers measure, can be given by using Rindler temperature of higher dimensional flat embeding space [23,24,25,26]. 1 l2 in order to perceive a temperature It is clear from (2.4) that the temperature which an observer with proper time τ measures is TRindler-AdS α 2π (2.5). It is easy to see that by making the changes ατ → iφ ,r → ρ and χ → it, the metric of Rindler-AdS transforms to the global coordinate These transformations are valid for the asymptotic Killing vectors and the generators of dual CFTs. the contraction of time in the global case changes to the contraction of space in the Rindler case
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